Shouldn't we be able to use Universal Links into Amazon on iOS? They are hosting this file: https://www.amazon.com/apple-app-site-association and this blog post seem to be certain of it. However, if I make a link that follows one of their site-association rules, such as
http://www.amazon.com/gp/product/0062273205,
I keep getting directed to Safari instead of the app. I have never clicked Back to X from the Amazon app, so it can't be that cache that is messing with me.